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Occurs in Blackburn. Complement (not yet in OEIS) is {7, 19, 25, 27, 31, 32, 34, 37, 39, 43, 45, 46, 47, 52, 55, ...}. Abstract: An n-ary k-radius sequence is a finite sequence of elements taken from an alphabet of size n such that any two distinct elements of the alphabet occur within distance k of each other somewhere in the sequence. These sequences were introduced by Jaromczyk and Lonc to model a caching strategy for computing certain functions on large data sets such as medical images.

Let f_k(n) be the shortest length of any k-radius sequence. We improve on earlier estimates for f_k(n) by using tilings and logarithms. The main result is that f_k(n) ~ n^2/(2k) as n tends to infinity whenever a certain tiling of Z^r exists. In particular this result holds for infinitely many k, including all k < 195 and all k such that k+1 or 2k+1 is prime [this sequence]. For certain k we get a sharper error term for infinitely many values of n, using the theory of logarithms.